You know, I kept re-reading your question and thinking, "That's a good question!" It probably differs from person to person, but I'll share what I consider stiff: When I can poke my finger against the icing that on the beater and none sticks to my finger.

we learned in our decorating classes that stiff buttercream is when you put your cake knife in the middle and it stands there,doesn't move at all. Medium consistency is when it starts falling a bit and soft (or whatever it's called) is when the knife falls over right away, nothing at all holding it up

You know, I kept re-reading your question and thinking, "That's a good question!" It probably differs from person to person, but I'll share what I consider stiff: When I can poke my finger against the icing that on the beater and none sticks to my finger.

this would be the closest to a description i could come up with too. Stiff buttercream is harder to pipe out of a bag, but it's not impossible. If you tried to ice an entire cake with stiff buttercream, when you tried to smooth it out it would most likely pull the cake up and around instead of smoothing out and giving it a nice even coat.

we learned in our decorating classes that stiff buttercream is when you put your cake knife in the middle and it stands there,doesn't move at all. Medium consistency is when it starts falling a bit and soft (or whatever it's called) is when the knife falls over right away, nothing at all holding it up

Yes this! I was taught the same thing!

And if you are making icing it usually starts as stiff and as you add more fluid you will get medium and then thin. Too thin, add more ps.